Algebra 2. Transformation of Fucntions.

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SUMMARY

The discussion clarifies the differences between vertical and horizontal compression in function transformations. Vertical compression "squishes" points towards the x-axis, with invariant points located on the x-axis, while horizontal compression "squishes" points towards the y-axis, with invariant points on the y-axis. An example provided is the function f(x) = 4x², which represents a vertical stretch by a factor of 2, but is also equivalent to a horizontal compression by a factor of 1/2.

PREREQUISITES
  • Understanding of function transformations
  • Familiarity with the concepts of vertical and horizontal shifts
  • Knowledge of invariant points in transformations
  • Basic algebra skills, particularly with quadratic functions
NEXT STEPS
  • Study the properties of function transformations in detail
  • Learn about the effects of different transformation factors on graphs
  • Explore the concept of invariant points in various transformations
  • Practice with examples of quadratic functions and their transformations
USEFUL FOR

Students studying Algebra 2, educators teaching function transformations, and anyone seeking to deepen their understanding of graph behavior under various transformations.

njkid
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Whats the difference between "Vertical Compression" and "Horizontal Compression"? Can you give me couple example? Thank you.
 
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A vertical compression is "squishing" all points towards the x-axis, it is also important to rember that the invariant points in such a transformation are ON the x-axis. A horizontal compression is "squishing" all points towards the y-axis. It is important to remember that all invariant points are on the y-axis. However, there are some cases where a transformation is equivalent to another transformation relative to a different axis.
Consider the function f(x) = 4x^2 This is a transformation of the graph of y = x^2 vertically stretched by a factor of 2. However, this is also equivalent to a horizontal compression by a factor of 1/2.
 
Thank you very much.
 

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